WASHINGTON — The Supreme Court began its new term this morning by turning away hundreds of appeals. The justices took the bench just past 10 a.m. even as much of the rest of the government was coping with a partial shutdown. Chief Justice John Roberts opened the new term without any reference to the partisan impasse over the budget and the new health care law that his vote helped uphold in 2012. The court has announced it will operate normally at least through the end of this week. The justices are hearing six arguments, including a challenge to limits on campaign contributions. Among the appeals denied today was Virginia Attorney General Ken Cuccinelli’s request to review a federal appeals court ruling that threw out Virginia’s anti-sodomy law. Ten years ago, the Supreme Court struck down the Texas anti-sodomy law in a case involving two adults. Virginia argued that the Texas ruling did not apply to sex acts between adults and minors. The court also declined to hear, at least for now, Argentina’s appeal of a ruling that orders it to pay hedge funds that bought up some of the country’s unpaid debt from its default in 2001. The country is continuing to pursue its case in federal court in New York and could file another appeal with the Supreme Court.